A forging press, for example an eccentric forging press or a screw press, usually has a machine frame that for a large press is made of solid or tubular columns that extend between and seated in fixed upper and lower transverse beams and that are clamped in place by tie rods. Such a press frame is described for example in U.S. Pat. No. 5,619,884. Tension bolts extend throughgoing bores in the upper and lower press traverse as well as through bores that extend through the full length of the columns and through the machine frame. This requires long bores that are complex to form in the press columns and long tie rods or press anchors with a large shank and thread diameter. Moreover, extensive mounting aids and increased crane elevation heights are necessary due to the special length of the tension bolts and to mount the long anchors. Furthermore, transporting the bolts also requires special precautions, since they must generally have a length that is greater than the overall height of the entire machine frame.